Irreversible Dynamics Research Articles

Target Search of Active Agents Crossing High Energy Barriers.

Target search by active agents in rugged energy landscapes has remained a challenge because standard enhanced sampling methods do not apply to irreversible dynamics. We overcome this nonequilibrium rare-event problem by developing an algorithm generalizing transition-path sampling to active Brownian dynamics. This method is exemplified and benchmarked for a paradigmatic two-dimensional potential with a high barrier. We find that even in such a simple landscape the structure and kinetics of the ensemble of transition paths changes drastically in the presence of activity. Indeed, active Brownian particles reach the target more frequently than passive Brownian particles, following longer and counterintuitive search patterns.

Far-away-from-equilibrium quantum-critical conformal dynamics: Reversibility, thermalization, and hydrodynamics

Generic far-away-from-equilibrium many-body dynamics involve entropy production, and hence are thermodynamically irreversible. Near quantum critical points, an emergent conformal symmetry can impose strong constraints on entropy production rates, and in some cases completely forbid entropy production, which usually occurs for systems that deviate from quantum critical points. In this article, we illustrate how the vanishing entropy production near a quantum critical point results in reversible far-away-from-equilibrium dynamics at finite temperatures that are otherwise irreversible. Away from the quantum critical point, the quantum dynamics are damped, and our analysis directly relates the thermalization time scale to the hydrodynamic viscosity near quantum critical points with dynamical critical exponent $z=2$. We demonstrate how both controllable reversible and irreversible dynamics can be potentially studied in cold gas experiments using Feshbach resonances.

Spectral theory of fluctuations in time-average statistical mechanics of reversible and driven systems

We present a spectral-theoretic approach to time-average statistical mechanics for general, non-equilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic stochastic dynamics with continuous or discrete state-space. We derive exact results for the mean, fluctuations and correlations of time average observables from the eigenspectrum of the underlying generator of Fokker-Planck or master equation dynamics, and discuss the results from a physical perspective. Feynman-Kac formulas are re-derived using It\^o calculus and combined with non-Hermitian perturbation theory. The emergence of the universal central limit law in a spectral representation is shown explicitly on large deviation time-scales. For reversible dynamics with equilibrated initial conditions we derive a general upper bound to fluctuations of occupation measures in terms of an integral of the return probability. Simple, exactly solvable examples are analyzed to demonstrate how to apply the theory. As a biophysical example we revisit the Berg-Purcell problem on the precision of concentration measurements by a single receptor. Our results are directly applicable to a diverse range of phenomena underpinned by time-average observables and additive functionals in physical, chemical, biological, and economical systems.

Matching theory to characterize sound emission during vortex reconnection in quantum fluids

In a concurrent work, Villois et al. 2020 reported the evidence that vortex reconnections in quantum fluids follow an irreversible dynamics, namely vortices separate faster than they approach; such time-asymmetry is explained by using simple conservation arguments. In this work we develop further these theoretical considerations and provide a detailed study of the vortex reconnection process for all the possible geometrical configurations of the order parameter (superfluid) wave function. By matching the theoretical description of incompressible vortex filaments and the linear theory describing locally vortex reconnections, we determine quantitatively the linear momentum and energy exchanges between the incompressible (vortices) and the compressible (density waves) degrees of freedom of the superfluid. We show theoretically and corroborate numerically, why a unidirectional density pulse must be generated after the reconnection process and why only certain reconnecting angles, related to the rates of approach and separations, are allowed. Finally, some aspects concerning the conservation of centre-line helicity during the reconnection process are discussed.

Single and double generator bracket formulations of multicomponent fluids with irreversible processes

The equations of reversible (inviscid, adiabatic) fluid dynamics have a well-known variational formulation based on Hamilton’s principle and the Lagrangian, to which is associated a Hamiltonian formulation that involves a Poisson bracket structure. However, real flows also include irreversible processes, such as viscous dissipation, heat conduction, diffusion and phase changes. Recent work has demonstrated that the variational formulation can be systematically extended to include irreversible processes and nonequilibrium thermodynamics, through the new concept of thermodynamic displacement. Irreversible processes have also been incorporated into the bracket structure through the addition of a dissipation bracket. This gives what are known as the single and double generator bracket formulations, which are the natural generalizations of the Hamiltonian formulation to include irreversible dynamics. Unlike the variational formalism, most of these bracket formalisms do not follow from a systematic construction and have often been derived via a case by case approach, with slightly different axioms used in different situations. In this paper, we show that the variational formulation yields a constructive and systematic way to derive from a unified perspective these bracket formulations for fully compressible, multicomponent, multiphase fluids with a single temperature and velocity. In the case of a linear relation between the thermodynamic fluxes and the thermodynamic forces, the metriplectic or GENERIC brackets are recovered. Many previous results in the literature, typically obtained via heuristic approaches, are demonstrated to be special cases of this general formulation.

Reciprocity relations in driven dissipative systems

Almost a century ago Onsager found a universal feature of all dissipative systems describing approach to thermodynamic equilibrium, the reciprocal relations. They hold for linear differential equations describing an evolution of macrovariables in vicinity of equilibrium states. It was assumed implicitly that underlying microdynamics is Hamiltonian and ergodic. The reversibility of Hamiltonian equations was one of the key features of microdynamics yielding Onsager’s relations. There are many situations where macrovariables, which are the slow parameters of microdynamics, describe, in fact, the mesoscopic phenomena. Thus, an additional course graining is to be done to get the equations of macroscopic theory. In particular, such are the problems of dislocation-mediated plasticity, where elimination of atomic degrees of freedom yields dislocation dynamics, and an additional averaging is needed to obtain the equations of macroscopic plasticity. This averaging problem is qualitatively different from the classical problems of nonequilibrium thermodynamics because the equations to be averaged are neither Hamiltonian nor ergodic, they are dissipative and irreversible. Besides, in driven systems there might be no equilibrium states. However, the basic question remains the same: Are there universal relations which the averaged equations must respect? In this paper, a positive answer to this question is given: the dependence of rates on forces must be potential in the limit of small and large forces. For small forces, this yields the relations which look quite similar to Onsager’s relations, though their origin caused by dissipative irreversible dynamics is quite different. In the limit of small forces a variational principle for dissipative potential is obtained; it reveals quite non-trivial reciprocities of macroscopic interactions. An immediate consequence of these results is the potentiality of the strain rate-stress constitutive relations in dislocation-mediated plasticity for small and large stresses. The reciprocity relations are illustrated by dislocation double-slip of a single crystal.

Nonreciprocal directional dichroism in multiferroics

Nonreciprocal directional dichroism in multiferroics, namely magnetoelectric coupling in the dynamic regime, is endowed with rich physics and promising applications, which are entangled with fundamental physical components, such as spin, orbital, lattice, charge, and topology. Such a linear nonreciprocal response behavior in the GHz-THz frequency range, represented by optical magnetoelectric effect and magnetochiral dichroism, occurs ubiquitously in material systems with the spontaneous breaking of space-time symmetry, and is subject to Onsager’s reciprocal theorem in the thermodynamic limit. Microscopically, these nonreciprocal responses are usually encoded by toroidization (chirality) and electromagnon (quasiparticle), thus establishing a comprehensive understanding of magnetoelectric coupling and irreversible dynamics. Herein, the basic mechanisms and emergent nonreciprocal directional dichroism in single-phase multiferroics are summarized. We expect that the present review will stimulate diverse possibilities toward nonreciprocal directional dichroism within and beyond multiferroics.

Open Quantum Dynamics Theory of Spin Relaxation: Application to μSR and Low-Field NMR Spectroscopies

An open quantum system refers to a system, which is in turn coupled to an environment that can describe time irreversible dynamics through which the system evolves toward the thermal equilibrium state. We present a quantum mechanically rigorous theory in order to help an analysis of spectra obtained from the advanced nuclear magnetic resonance (NMR) and muon spin rotation, relaxation or resonance ($\mu$SR) techniques. Our approach is based on the numerically "exact" hierarchical equations of motion (HEOM) approach, which allows us to study the reduced system dynamics for non-perturbative and non-Markovian system-bath interactions at finite temperature even under strong time-dependent perturbations. We demonstrate the present theory to analyze $\mu$SR and low-field NMR spectra, as an extension of the Kubo-Toyabe theory focusing on the effects of temperature and anisotropy of a local magnetic field, to help further the development of these experimental means.

The past shall not begin: Frozen seeds, extended presents and the politics of reversibility

The article analyzes the Svalbard Global Seed Vault (SGSV) as a specific security technology created to deal with the ecological threat of biodiversity loss. Built in 2008 inside the Arctic Circle, the SGSV serves as a backup for 1,700 agricultural gene banks around the world. If seed collections are lost due to natural disasters or human error, the gene banks can request copies of their varieties from Svalbard and restore their collections to continue the endeavour of plant breeding. The article focuses on the particular temporal politics expressed in the SGSV. Drawing on Niklas Luhmann’s reflections on time, it is argued that the SGSV opens up the possibility of reversing events by expanding the duration of the present. By separating seeds from their ecological connections on the one hand and controlling their metabolic processes through the use of cold on the other, an enduring temporal zone is created that allows modern society to control the unpredictable and irreversible dynamics of life and undo its emergent effects. The SGSV therefore materializes what is herein called the politics of reversibility.

Chaos and periodicities in a climatic time series of the Iberian Margin.

We analyze the time series of the temperature of the sedimentary core MD01-2443 originating from the Iberian Margin with a duration of 420 kyr. The series has been tested for unit-root and a long term trend is estimated. We identify four significant periodicities together with a low climatic activity every 100 kyr, and these were associated with internal and external forcings. Also, we identify a high-frequency fast component that acts on top of a nonlinear, irreversible slow-changing dynamics. We find the presence of chaos in the climate of the Iberian Margin by means of a neural network asymptotic test on the largest Lyapunov exponent. The analysis suggests that the chaotic dynamics is associated with the fast high-frequency component. We also carry out a statistical analysis of the dimensionality of the attractor. Our results confirm the possibility that periodic behavior and chaos may coexist on different time scales. This could lead to different degrees of predictability in the climate system according to the characteristic time scales and/or phase-space locations.

Ultrafast electron dynamics in monolayer MoS2 interacting with optical pulse influenced by exchange field and waveform

In this paper, we investigate the effect of waveform and carrier-envelope phase on the electron dynamics in monolayer MoS2 interacting with an ultrashort (few-femtosecond) optical pulse in the presence of magnetic exchange field. The waveform of the zero area pulse is characterized by Hermite–Gaussian polynomials associated with time-dependent and carrier-envelope phases. Because the duration of optical pulse is less than the characteristic electron scattering time (10–100 fs), the electron dynamics is coherent, and can be described by the time-dependent Schrödinger equation. We show, that the electron transition from valence band to conduction band is a deeply irreversible dynamics, which implies quantum electron dynamics is highly nonadiabatic. We study the effect of carrier-envelope phase and exchange field on the conduction band population for two types of waveform. Electron distribution in reciprocal space gives asymmetric hot spots in different K and K′ valleys after the pulse ends (valley polarization effect), which is found to be more sensitive to carrier-envelope phase. The predicted effect provides new opportunities for the improvement of information processing in the petahertz domain and optoelectronics applications.

"Systematic Semiotic Organisation and Anthropologisation of the Science of Soul - Towards Cultural Psychology".

Zagaria et al. identified fundamental issues and inconsistencies in the understanding of the fundamentals of psychological science. This paper attempts to trace the roots of the inconsistency and incompleteness of definitions of basic psychological concepts in the historical development of psychological science that led to the fragmentation of psychology into the various reductionistic and monological "schools of thoughts". A systematic approach is proposed as a way for a reconsideration of the understanding of mental processes in a holistic way that could serve as the starting point for the proper theoretical reflection of the catalytic interplay between subjective (intentionality), situational and cultural factors. It is argued that the anthropologisation of psychology and bringing back the focus on phenomenological aspects of experiencing which are characterised by intra-individual, cross-situational and inter-cultural variety is especially significant for the rebuilding of the integrity of psychology. The principle of "organic selection" is proposed as the basis for individual subjectivity and innovations throughout the irreversible ontogenetic developmental dynamics that allows individuals to jump beyond the phylogenetically prescribed schemata.

Coherent electron dynamics in monolayer MoS2 under ultrashort optical pulse

A theoretical investigation on the coherent Dirac-like quasiparticle dynamics in monolayer $\text{MoS}_2$ under an ultrashort optical pulse irradiation is presented. Particularly, we remain specific features of ML-MDS associated with the mass asymmetry $\alpha$ and topological aspect $\beta$ parameters resulting in Schr$\stackrel{..}{\text{o}}$dinger type wavevector of charge carriers. The direct band gap, spin-resolved valence band spilitting and valley degeneracy breaking due to strong spin-orbit coupling affect ultrafast dynamics of Dirac fermions. Because the duration of the optical pulse is less than the electron scattering time, which is $\sim 10-100\ fs$, the electron dynamics in electric field of the optical pulse is coherent, and consequently, we can describe the coupling of electron with strong electromagnetic field by the time-dependent Schr$\stackrel{..}{\text{o}}$dinger equation. The conduction band and valence band coupling via the strong electric field of pulse ($0.2-2.5 \ V/\text{\AA}$) gives rise to appearance of a dipole moment during the pulse is applied. We find that the dipole is complex, originating from the existence of band gap. We show an asymmetric singularities in Dirac points for absolute of dipole moment. We solve the resulting coupled evolution equations for the expansion coefficient of valence and conduction bands to obtain probability of population transition between valence and conduction bands. The irreversible electron dynamics as a key feature of two-dimensional Dirac matters in interacting with an ultrashort pulse strongly depends on the electronic structure of $\text{MoS}_2$. Furthermore, we present conduction band population distribution with an asymmetric exhibition at the each pair of Dirac points ($K$ and $K'$), when the pulse ends. This leads to valley polarization effect.

A new continuum model for general relativistic viscous heat-conducting media.

The lack of formulation of macroscopic equations for irreversible dynamics of viscous heat-conducting media compatible with the causality principle of Einstein's special relativity and the Euler-Lagrange structure of general relativity is a long-lasting problem. In this paper, we propose a possible solution to this problem in the framework of SHTC equations. The approach does not rely on postulates of equilibrium irreversible thermodynamics but treats irreversible processes from the non-equilibrium point of view. Thus, each transfer process is characterized by a characteristic velocity of perturbation propagation in the non-equilibrium state, as well as by an intrinsic time/length scale of the dissipative dynamics. The resulting system of governing equations is formulated as a first-order system of hyperbolic equations with relaxation-type irreversible terms. Via a formal asymptotic analysis, we demonstrate that classical transport coefficients such as viscosity, heat conductivity, etc., are recovered in leading terms of our theory as effective transport coefficients. Some numerical examples are presented in order to demonstrate the viability of the approach. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.

Structure-preserving integrators for dissipative systems based on reversible- irreversible splitting.

We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible–irreversible coupling). We present a frame-work to construct structure-preserving integrators by splitting the system into reversible and irreversible dynamics. The reversible part, which is often degenerate and reduces to a Hamiltonian form on its symplectic leaves, is solved by using a symplectic method (e.g. Verlet) with degenerate variables being left unchanged, for which an associated modified Hamiltonian (and subsequently a modified energy) in the form of a series expansion can be obtained by using backward error analysis. The modified energy is then used to construct a modified friction matrix associated with the irreversible part in such a way that a modified degeneracy condition is satisfied. The modified irreversible dynamics can be further solved by an explicit midpoint method if not exactly solvable. Our findings are verified by various numerical experiments, demonstrating the superiority of structure-preserving integrators over alternative schemes in terms of not only the accuracy control of both energy conservation and entropy production but also the preservation of the conformal symplectic structure in the case of linearly damped systems.

Quantum master equations for a system interacting with a quantum gas in the low-density limit and for the semiclassical collision model

A quantum system interacting with a dilute gas experiences irreversible dynamics. The corresponding master equation can be derived within two different approaches: The fully quantum description in the low-density limit and the semiclassical collision model, where the motion of gas particles is classical whereas their internal degrees of freedom are quantum. The two approaches have been extensively studied in the literature, but their predictions have not been compared. This is mainly due to the fact that the low-density limit is extensively studied for mathematical physics purposes, whereas the collision models have been essentially developed for quantum information tasks such as a tractable description of the open quantum dynamics. Here we develop and for the first time compare both approaches for a spin system interacting with a gas of spin particles. Using some approximations, we explicitly find the corresponding master equations including the Lamb shifts and the dissipators. The low density limit in the Born approximation for fast particles is shown to be equivalent to the semiclassical collision model in the stroboscopic approximation. We reveal that both approaches give exactly the same master equation if the gas temperature is high enough. This allows to interchangeably use complicated calculations in the low density limit and rather simple calculations in the collision model.

Modeling irreversible molecular internal conversion using the time-dependent variational approach with sD2 ansatz.

Effects of non-linear coupling between the system and the bath vibrational modes on the system internal conversion dynamics are investigated using the Dirac-Frenkel variational approach with a newly defined sD2 ansatz. It explicitly accounts for the entangled system electron-vibrational states, while the bath quantum harmonic oscillator states are expanded in a superposition of quantum coherent states. Using a non-adiabatically coupled three-level model, we show that efficient irreversible internal conversion due to quadratic vibrational-bath coupling occurs when the initially populated system vibrational levels are in resonance with the vibrational levels of a lower energy electronic state, also, a non-Gaussian bath wavepacket representation is required. The quadratic system-bath couplings result in broadened and asymmetrically squeezed bath quantum harmonic oscillator wavepackets in the coordinate-momentum phase space.

Irreversible structural dynamics on the surface of bimetallic PtNi alloy catalyst under alternating oxidizing and reducing environments

In this work changes in surface chemistry and morphology of PtNi alloy induced by redox environments were investigated by photoelectron spectroscopy, atomic force microscopy and substantiated by theoretical calculations. PtNi was exposed to alternating oxidation (O2) and reduction (H2) gaseous atmospheres at different temperatures (298, 373, 523 K) to simulate its behavior as a cathode catalyst in proton exchange membrane fuel cells.Results showed that the PtNi alloy undergoes surface nickel enrichment under switched reactive environments. The most significant effects occurred at 523 K, when the Ni/Pt surface atomic ratio increased from 0.8 to 6.7 after five redox cycles, while the bulk Ni/Pt value reached 2.3. Along with compositional changes catalyst coarsening was observed.The revealed behavior of the PtNi alloy allows a better understanding of the structural dynamics of a bimetallic catalyst during its interaction with reactive environments that is a prerequisite for development of efficient fuel cell catalyst.

Multisite Daily Streamflow Simulation With Time Irreversibility

AbstractSynthetic daily streamflow generation requires a critical understanding of the underlying dynamics resulting from the inherent temporal asymmetry (time irreversibility) in the rising and falling limbs of the hydrograph. Most models considering the time irreversibility deal with single‐site streamflow simulation. Addressing intersite dependencies is, however, crucial for interconnected stream networks. This study presents a time irreversibility dynamics‐based multisite streamflow generating framework to simulate concurrent streamflow sequences at multiple sites in a basin. This framework explicitly takes into account the spatial correlation and time irreversible dynamics of streamflow. To demonstrate the utility and applicability, a few selected streamflow gauging stations in the Godavari River Basin, located in southern India, are considered. The proposed framework shows the ability to adequately generate multisite simulations capturing at‐site statistics as well as intersite correlations for the case study. Furthermore, the approach ensures that the simulated flow values are not merely resampled from the historical data, uses the physical features of the hydrograph, and shows variability beyond that observed in the historical sequence. Such a rich variety of streamflow sequences can help water managers to investigate how existing water resources systems on interconnected stream networks will operate in scenarios which have not been observed in the historical record.

In silico simulation of reversible and irreversible swelling of mitochondria: The role of membrane rigidity

Mitochondria have been widely accepted as the main source of ATP in the cell. The inner mitochondrial membrane (IMM) is important for the maintenance of ATP production and other functions of mitochondria. The electron transport chain (ETC) generates an electrochemical gradient of protons known as the proton-motive force across the IMM and thus produces the mitochondrial membrane potential that is critical to ATP synthesis. One of the main factors regulating the structural and functional integrity of the IMM is the changes in the matrix volume. Mild (reversible) swelling regulates mitochondrial metabolism and function; however, excessive (irreversible) swelling causes mitochondrial dysfunction and cell death. The central mechanism of mitochondrial swelling includes the opening of non-selective channels known as permeability transition pores (PTPs) in the IMM by high mitochondrial Ca2+ and reactive oxygen species (ROS). The mechanisms of reversible and irreversible mitochondrial swelling and transition between these two states are still unknown. The present study elucidates an upgraded biophysical model of reversible and irreversible mitochondrial swelling dynamics. The model provides a description of the PTP regulation dynamics using an additional differential equation. The rigidity tensor was used in numerical simulations of the mitochondrial parameter dynamics with different initial conditions defined by Ca2+ concentration in the sarco/endoplasmic reticulum. We were able to estimate the values of the IMM rigidity tensor components by fitting the model to the previously reported experimental data. Overall, the model provides a better description of the reversible and irreversible mitochondrial swelling dynamics.